Integral mean curvature analysis of 3D grain growth: Linearity of dV/dt and grain volume

The volumetric growth rate of individual grains has been found to be directly proportional to the individual grain volume V as dV/dt = β(Vo -V). This simple result is explained through the DeHoff relationship dV/dt = −kMs between growth rate and the integral mean curvature of individual grains, M s , combined with the experimentally observed relationship between M s and grain volume, M s = α(Vo -V). These relationships have now been observed consistently in both 3D grain growth simulations and experiments. This paper describes the relationships among these kinetic and geometric grain characteristics that provide this simple description of 3D grain growth.